The iterative method for solving nonlinear matrix equation X s + A ∗ X − t A = Q
Nonlinear matrix equation X s + A ∗ X − t A = Q, where Q is an Hermitian positive definite matrix, A ∗ is the conjugate transpose of the matrix A and both of s and t are positive integers, has widely applied background. In this paper, necessary conditions and sufficient conditions for the existence...
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Published in | Applied mathematics and computation Vol. 188; no. 1; pp. 46 - 53 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
01.05.2007
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Subjects | |
Online Access | Get full text |
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Summary: | Nonlinear matrix equation
X
s
+
A
∗
X
−
t
A
=
Q, where
Q is an Hermitian positive definite matrix,
A
∗ is the conjugate transpose of the matrix
A and both of
s and
t are positive integers, has widely applied background. In this paper, necessary conditions and sufficient conditions for the existence of Hermitian positive definite solutions of this equation are derived. An iterative method for obtaining Hermitian positive definite solutions is proposed. Moreover, a perturbation bound for the Hermitian positive definite solutions is given. |
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ISSN: | 0096-3003 1873-5649 |
DOI: | 10.1016/j.amc.2006.09.085 |